Question

# A small store keeps track of the number X of customers that make a purchase during...

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution.

 X 0 1 2 3 4 P(X) 0.1 0.1 0.1 0.6

Determine P(x=2):

Determine P(x≥3):

Determine P(x<3):

Determine the mean number of customers:

Determine the standard deviation of the number of customers

Solution :

The sum of the probability is equal to 1 .

P(X) = 1

(a)

P(x = 2) = 1 - 0.1 - 0.1 - 0.1 - 0.6 = 0.1

(b)

P(x 3) = P(x = 3) + P(x = 4) = 0.1 + 0.6 = 0.7

(c)

P(x < 3) = P(x = 0) + P(x = 1) + P(x = 2) = 0.1 + 0.1 + 0.1 = 0.3

(d)

 x P(x) x * P(x) x2 * P(x) 0 0.1 0 0 1 0.1 0.1 0.1 2 0.1 0.2 0.4 3 0.1 0.3 0.9 4 0.6 2.4 9.6 Sum 1 3 11

Mean = = X * P(X) = 3

(e)

Standard deviation =

=X 2 * P(X) - 2

=  11 - 32

= 1.4142

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